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# What is the sum of the digits of integer x, where x = 4^10* 5^13?

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Math Expert
Joined: 02 Sep 2009
Posts: 59712
What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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05 Nov 2017, 02:38
1
11
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Difficulty:

45% (medium)

Question Stats:

65% (01:39) correct 35% (01:42) wrong based on 205 sessions

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What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

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Joined: 18 May 2016
Posts: 180
Location: India
GMAT 1: 710 Q48 V40
WE: Marketing (Education)
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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05 Nov 2017, 02:58
3
X= 2^20*5^13
= 10^13 *2^7
= 128*10^13

Sum of digits = 11
Option B

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Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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05 Nov 2017, 12:15
2
2
Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

Answer is B as follows

$$x = 4^{10} * 5^{13} = 2^{20}*5^{13} = 10^{13}*2^7 = 10^{13}*128$$
Sum of the digits = 1+2+8 = 11

Hence B
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Joined: 26 Jan 2017
Posts: 3
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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07 Nov 2017, 09:05
3
Since we are looking for the sum of the digits we can simplify this problem by removing the trailing zeros (zeros at the end of the number). Trailing zeros are added to a number when multiplied by 10.

Remember 10 = 2 * 5
Thus, in our problem 4^10*5^13 or:
2^20 * 5^13

As you can see we have the pair 2*5 thirteen times. We can remove 2^13 and 5^13 and work with the rest which is 2^7 = 128

1+2+8 = 11
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Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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08 Nov 2017, 17:35
4
Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

We can simplify the given equation:

x = 4^10 x 5^13

x = 2^20 x 5^13

x = 2^7 x 2^13 x 5^13

x = 2^7 x 10^13

x = 128 x 10^13

We see that x is the number 128 followed by 13 zeros. Thus, the sum of the digits of x is 1 + 2 + 8 = 11.

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# Jeffrey Miller

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Posts: 49
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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04 Apr 2019, 05:59
1
we can use the concept of cyclicity to find out the units digit.
units digit of 4^10 is 6 and units digit of 5^13 is 5
6+5 = 11
units digit 1.
(This method works because there is no repetition of units digit in the options.)
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Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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07 Apr 2019, 19:04
1
Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

We can rewrite the expression as:

2^20 x 5^13

2^7 x 2^13 x 5^13

2^7 x 10^13

128 x 10^13

This is the number 128 followed by 13 zeros, so the sum of the digits is 1 + 2 + 8 = 11 (note: the 13 zeros will not contribute anything to the sum).

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# Scott Woodbury-Stewart

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Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?   [#permalink] 07 Apr 2019, 19:04
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# What is the sum of the digits of integer x, where x = 4^10* 5^13?

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